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Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $\frac{1}{4}$
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$-\frac{1}{2}\ln\left(x\right)+\ln\left(\sqrt[4]{x^2+4}\right)$
Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression -1/2ln(x)+1/4ln(x^2+4). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \frac{1}{4}. Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right).